Pages

Monday, November 7, 2011

Squib on adverbial “at all”

As a general rule, adverbial “at all” can be used only when all of the following hold:

The sentence is about degree, location, number, or type.

The sentence is negative.

If the sentence is about location, number, or type, its logical form is particularly quantified. Quantification is irrelevant to sentences about degree.

For instance...I don’t like mushrooms at all. [aboutness: degree, charge: negative]There are no dogs in heaven at all. [aboutness: location, charge: negative, quantification: particular]There are no coins in my purse at all. [aboutness: number, charge: negative, quantification: particular]*There are coins in my purse at all. [aboutness: number, charge: positive, quantification: particular]*There isn’t every coin in my purse at all. [aboutness: number, charge: negative, quantification: general]There is one exception to this: when uttered in a counterfactual context, “any x at all” appends well formed formulae to yield new wff’s whenever x acts as a noun or noun phrase. The gramaticallity of this construction depends only on the counterfactual status and not on positivity, quantity, or aboutness. You might have been any animal at all.Unicorns could live anywhere at all. (where “where” acts as a noun)There couldn’t be any man who breathes air in space at all.The quantity of “unicorns could live anywhere at all” is actually generalization of a particular. In fact, it would seem that the quantity of all counterfactual sentences with adverbial “at all” is nested. At all is a sticky problem for semanticians, because in order to understand what’s really going on we’re going to have to work out words like “could”.What exactly is the problem with “could”? The problem is the truth value of sentences containing it. “Unicorns could live anywhere at all,” seems to be asserting the truth of the intended proposition just like any other statement, but if the characteristic function for the truth value of counterfactuals in the actual world exists, it is inaccessible. It’s not that we don’t know the graph of the relevant function because cataloging all the things of such and such a class along with their truth conditions is impractical or would take an infinite amount of time--it’s that such a process can’t even begin for the class of non-actualized possibilities. Therefore, semanticians trying to hang out in some kind of formalistic limbo will have to take a metaphysical stance on the nature of semantic practice to work out the meaning of counterfactuals and by extension the meaning of “at all”.I see a few options for rendering “at all” meaningful.

Platonism (aka “the lazy way out”): the sentence has a truth value of true or false and the characteristic function exists mind-independently. “Unicorns could live anywhere at all” means that the proposition to which it refers exists in Plato’s heaven. It doesn’t matter that we can’t know the function’s graph; we can employ the function intentionally anyway.

Modal realism: the sentence has a truth value of true or false and the characteristic funciton exists mind-independently. “Unicorns could live anywhere at all” means that for every place in the actual world there exists a possible world containing a counterpart of that place and at least one unicorn lives in it. As above, we can use the function without being able to know its graph.

Conceptual semantics: much like modal realism, but fully mind-dependent. “Unicorns could live anywhere at all” means that the pluriverse existing representationally in the mind of the speaker is such that the modal realistic interpretation is represented as true (and no relationship to a mind-independent pluriverse is relevant).

Intuitionism: the truth value needn’t be either “true” or “false”, in which case we get to keep sober realism and counterfactuals are unproblematic. Obviously, this would mean a complete overhaul of semantics to account for a non-finite t domain. I say we go for it. Any takers?